Figure 1: Leading EOF of monthly geopotential anomalies north of 20º at each level.
The Northern Annular Mode is the leading EOF of NH circulation. Here, shown as the leading EOF of monthly geopotential height anomalies between 1979 and 2000 at 1000 hPa, following the CPC methodology. I will also compute the leading EOF at 200 hPa and 50 hPa to get a sense of how this changes vertically.
Figure 1: Leading EOF of monthly geopotential anomalies north of 20º at each level.
The leading EOF at 1000 hPa is not really all that “annular”. It’s actually a positive anomaly over the Arctic and two negative anomalies over the northern Atlantic and Northern Pacific (or vice versa depending on the sign). Leading EOFs at higher levels do become more annular.
The question is, are the higher latitude anomalies co-occurring? In other words, is this an hemispheric pattern or is it two relatively independent patterns –the Atlantic and Pacific anomalies– that are mixed into a single EOF?
To look into this question I compute the leading EOF of these same data, but using overlapping 90º segments centred at each longitude. This results into 144 local EOFS, one at each longitude. If the NAM is an hemispheric phenomena, then all these indices should be fairly well correlated with each other. On the other hand, if it is a mix of different local modes, then we would expect to see a lack of correlation between separated longitudes.
The next figure shows the result of plotting the central part of each local EOF. The result fits the NAM pattern really well.
Figure 2: Leading EOF computed at 90º chunks centred at each longitude (shaded) and leading EOF computed using the whole domain (contours).
Now, I compute the cross-correlation between all pairs of indices, which is shown in the next figure.
Figure 3: Cross-correlation between the time series of each local EOF. The boxes in the third panel group longitudes into coherent sections based on hierarchical clustering. Background map of the Northern Hemisphere for reference.
At 1000 hPa there are two (or three) clearly delineated regions that have high intra-correlation but low inter-correlation
So, for example, local EOFS in the Pacific sector share correlations above 0.8 among themselves, but low (0.2–0.3) correlations with EOFs in the Atlantic sector and no correlation (< 0.2) with EOFs in the Eurasian sector.
This strongly suggest that there are there relatively independent modes of variability instead of a single hemispheric mode. EOFs in the Eurasian sector are not as highly correlated among themselves as the other two, so they might not form a single robust area of joint variability.
Higher levels are not as clustered.
Local EOFs at 200 hPa show some vestigial elements of the correlation structure at 1000 hPa but is not as clear. What it is clearer is the lack of correlation between the Pacific and Eurasian sectors.
Local EOFs at 50 hPa seem to be well correlated along the whole hemisphere. The minimum correlation is between North America and European local EOFs, but even those are a very respectable 0.4. This suggests a more robust hemispheric mode that could easily earn the “Northern Annular Mode” designation.
This regionalisation of the local EOFs at 1000 hPa is broadly applicable to all trimesters, as shown in the next figure.
Figure 4: Same as the previous figure but by trimester and only for 1000 hPA.
The next figure shows the correlation between geopotential height anomalies at 1000 hPa and these regional EOFs defined as the mean index of the local EOFs belonging to that region.
Figure 5: Correlation between 1000 hPa regional EOF indices computed as the mean indices of local EOFs at 1000 hPa belonging to that region and geopotential height at different levels (shaded) and the NAM pattern (contours). (i.e. the 50 hPa level is the correlation between 50 hPa geopotential height and the 1000 hPa regional EOF, not the 50 hPa regional EOF.)
Looking first at the relationship at 1000 hPa (i.e. the same level as the computed index), each regional EOFs is associated with geopotential anomalies only in their respective regions and there is little to no correlation outside each region. Interestingly, each seem to map relatively well to the corresponding features of the NAM pattern, shown in contours.
The Atlantic EOF shows negative anomalies in the northern Atlantic and positive anomalies in the polar regions, which are co-located with the corresponding NAM anomalies. Notably, it is not associated with significant anomalies in the northern Pacific. The polar anomalies do not extent so much to the south in the Eurasian sector. Conversely, the Pacific EOF is associated with negative anomalies in the North Pacific and some (but weak) positive anomalies in the polar regions. Again, these are co-located with the corresponding NAM anomalies but lack the anomalies in the northern Pacific. There is an extra area of negative anomalies east of North America which fall outside the Pacific sector and doesn’t have correspondence in the NAM pattern.
Finally the Eurasian EOF is associated with positive anomalies in high latitudes, centred in the Kara and Barents seas which corresponds to an area of positive anomalies in the NAM pattern that is not fully explained by the anomalies associated with the Atlantic EOF. At higher latitudes, it’s associated with negative anomalies over Europe. This further suggest the independent nature of these three (or two) different modes of variability that are mixed in the NAM.
The relationship between the regional 1000 hPa EOFs and geopotential height at 200 hPa follows a similar story but with smoother patterns. The correlation pattern with the Pacific region EOF shows a more evident wave train at this level, which probably betrais that the PNA is probably responsible of this regional EOF.
At 50 hPa, the correlations with the 1000 hPa regional indices are basically zonally symmetrical for the Atlantic and Eurasian regional EOFs, but much less so the the Pacific regional EOF, which has two negative correlations over the Pacific and over Europe and very weak positive correlations over the Arctic.
This suggests that the leading EOF at the lower stratosphere, which is a proper annular mode, is not associated with an annular mode in the troposphere, but with the regional Atlantic and Eurasian modes (remmebering that the latter is not as well defined as the former).
For a further example of how disparate these modes can be, the next figure shows the correlation between each local EOF and the ONI index, showing that the Atlantic EOF is moderately correlated with ENSO, but not the local EOFs outside of this region.
Figure 6: Correlation between each local EOF and the Oceanic Niño Index (ONI). The horizontal dashed line marks the correlation between the NAM and the ONI.
